A sum of money placed at compound interest double itself in 3 years. In how many years will it amount to eight times itself?

⇒ Let, Principal be Rs. x then Amount = Rs. 2x, Rate = r% and Time (n) = 3 years.

⇒ A = P × [1 + (r/100)]n

⇒ 2x = x × [1 + (r/100)] 3

⇒ 2 = [1 + (r/100)] 3 ------ 1

⇒ If sum become 8 times in the time n years then,

⇒ 8 = [1 + (r/100)] n

⇒ 23 = [1 + (r/100)] n

⇒ putting the value of equation 1 into above we get,

⇒ ([1 + (r/100)] 3)3 = [1 + (r/100)] n

∴ n = 9